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<p>We investigate homological invariants arising from the linear strand of Wollastonite graphs. In particular, we derive combinatorial formulas for the Castelnuovo-Mumford regularity, the projective dimension, and the initial graded Betti numbers of the edge ideals of these graphs. Furthermore, we express the remaining Betti numbers of these edge ideals in terms of the Hilbert series associated with the <i>i</i>-dimensional faces of their corresponding simplicial complexes. Finally, we show that the edge ring of a Wollastonite graph is not Cohen-Macaulay.</p>

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Homological invariants of edge ideals of Wollastonite graphs

  • 期刊论文

  • 发表日期：

    2026年4月11日

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  • Bilal Ahmad Rather

摘要

We investigate homological invariants arising from the linear strand of Wollastonite graphs. In particular, we derive combinatorial formulas for the Castelnuovo-Mumford regularity, the projective dimension, and the initial graded Betti numbers of the edge ideals of these graphs. Furthermore, we express the remaining Betti numbers of these edge ideals in terms of the Hilbert series associated with the i-dimensional faces of their corresponding simplicial complexes. Finally, we show that the edge ring of a Wollastonite graph is not Cohen-Macaulay.